The receiver should be placed at the focus of the parabolic dish for best reception, because the incoming signal will be concentrated at the focus.
We place the vertex of the parabola at the origin (for convenience) and use the equation of the parabola to get the focal distance (p) and hence the required point.
In general, the equation for a parabola with vertical axis is
`x^2 = 4py.`
We can see that the parabola passes through the point `(6, 2)`.
Substituting, we have:
`(6)^2 = 4p(2)`
So `p = 36/8 = 4.5`
So we need to place the receiver 4.5 metres from the vertex, along the axis of symmetry of the parabola.
The equation of the parabola is:
`x^2 = 18y `
`y = x^2 /18`
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